Mass subjected to a radial force will accelerate. Rotations and gyrations are two techniques to induce radial force. Gyration induced acceleration of a mass by a structure moving in a gyration mode is well understood; water inside a Hula Hoop is an example of a mass accelerated by the hoop structure which in turn is driven by a child's gyrating body. See for example U.S. Pat. No. 5,699,779. Simplified equations of motion for the mass reduce to a phase lock solution if initial conditions are satisfied. Satisfying the Hula-Hoop initial conditions to phase lock the water to the structure involves a ramping up in gyration frequency and gyration radius for the Hula Hoop. More complex mathematical equations include friction and drag, and produce a motion for the mass that is “approximately” phase locked with a slight oscillatory motion (small acceleration and small de-acceleration). Deliberately exaggerating this oscillatory behavior by means other than friction and drag is possible; mismatch of the velocity is an obvious example. A simple example is demonstrated by inserting a ball bearing into a gyrating system with different insertion velocities, the gyrating system either increases the ball's velocity or decreases the ball's velocity to phase lock it to the moving structure. These accelerations (changes in velocity) can be exploited in numerous ways.
Other gyration systems use a fixed pathway length, a fixed radius of gyration, or fixed gyration frequency, or the combination, resulting in a limited range of performance and highly restrictive initial conditions for phase stabilized acceleration.
In any phase-locked system the perfect analytical solution allows for “corrections” if the stable condition is slightly disturbed. The range of angular offset, generated by position shifts caused by routing changes, for which a stable condition can be recovered reflects into the region of pathway adjustments that will be the focus of this application.